Emergence in games

The future direction of game development is towards more flexible, realistic, and interactive game worlds. However, current methods of game design do not allow for anything other than pre-scripted player exchanges and static objects and environments. An emergent approach to game development involves the creation of a globally designed game system that provides rules and boundaries for player interactions, rather than prescribed paths. Emergence in Games provides a detailed foundation for applying the theory and practice of emergence in games to game design. Emergent narrative, characters and agents, and game worlds are covered and a hands-on tutorial and case study allow the reader to the put the skills and ideas presented into practice.

Objectifying early-number : a visual nomenclature to express mathematical domain knowledge

To address issues of divisive ideologies in the Mathematics Education community and to subsequently advance educational practice, an alternative theoretical framework and operational model is proposed which represents a consilience of constructivist learning theories whilst acknowledging the objective but improvable nature of domain knowledge. Based upon Popper’s three-world model of knowledge, the proposed theory supports the differentiation and explicit modelling of both shared domain knowledge and idiosyncratic personal understanding using a visual nomenclature. The visual nomenclature embodies Piaget’s notion of reflective abstraction and so may support an individual’s experience-based transformation of personal understanding with regards to shared domain knowledge. Using the operational model and visual nomenclature, seminal literature regarding early-number counting and addition was analysed and described. Exemplars of the resultant visual artefacts demonstrate the proposed theory’s viability as a tool with which to characterise the reflective abstraction-based organisation of a domain’s shared knowledge. Utilising such a description of knowledge, future research needs to consider the refinement of the operational model and visual nomenclature to include the analysis, description and scaffolded transformation of personal understanding. A detailed model of knowledge and understanding may then underpin the future development of educational software tools such as computer-mediated teaching and learning environments.

A Popperian consilience : modelling mathematical knowledge and understanding

Goldin (2003) and McDonald, Yanchar, and Osguthorpe (2005) have called for mathematics learning theory that reconciles the chasm between ideologies, and which may advance mathematics teaching and learning practice. This paper discusses the theoretical underpinnings of a recently completed PhD study that draws upon Popper’s (1978) three-world model of knowledge as a lens through which to reconsider a variety of learning theories, including Piaget’s reflective abstraction. Based upon this consideration of theories, an alternative theoretical framework and complementary operational model was synthesised, the viability of which was demonstrated by its use to analyse the domain of early-number counting, addition and subtraction.

Which way from here? The spatiality of maps & navigation in first-person single-player video games

Player experience of spatiality in first-person, single-player games is informed by the maps and navigational aids provided by the game. This project uses textual analysis to examine the way these maps and navigational aids inform the experience of spatiality in Fallout 3, BioShock and BioShock 2. Spatiality is understood as trialectic, incorporating perceived, conceived and lived space, drawing on the work of Henri Lefebvre and Edward Soja. The most prominent elements of the games’ maps and navigational aids are analysed in terms of how they inform players’ experience of the games’ spaces. In particular this project examines the in-game maps these games incorporate, the waypoint navigation and fast-travel systems in Fallout 3, and the guide arrow and environmental cues in the BioShock games.

Clinical strategies for the alleviation of contractures from a predictive mathematical model of dermal repair

Hypertrophic scars arise when there is an overproduction of collagen during wound healing. These are often associated with poor regulation of the rate of programmed cell death(apoptosis) of the cells synthesizing the collagen or by an exuberant inflammatory response that prolongs collagen production and increases wound contraction. Severe contractures that occur, for example, after a deep burn can cause loss of function especially if the wound is over a joint such as the elbow or knee. Recently, we have developed a morphoelastic mathematical model for dermal repair that incorporates the chemical, cellular and mechanical aspects of dermal wound healing. Using this model, we examine pathological scarring in dermal repair by first assuming a smaller than usual apoptotic rate for myofibroblasts, and then considering a prolonged inflammatory response, in an attempt to determine a possible optimal intervention strategy to promote normal repair, or terminate the fibrotic scarring response. Our model predicts that in both cases it is best to apply the intervention strategy early in the wound healing response. Further, the earlier an intervention is made, the less aggressive the intervention required. Finally, if intervention is conducted at a late time during healing, a significant intervention is required; however, there is a threshold concentration of the drug or therapy applied, above which minimal further improvement to wound repair is obtained.

Proximity-to-goal as a constraint on patterns of behaviour in attacker–defender dyads in team games

The aim of this study was to determine whether spatiotemporal interactions between footballers and the ball in 1 vs. 1 sub-phases are influenced by their proximity to the goal area. Twelve participants (age 15.3 ± 0.5 years) performed as attackers and defenders in 1 vs. 1 dyads across three field positions: (a) attacking the goal, (b) in midfield, and (c) advancing away from the goal area. In each position, the dribbler was required to move beyond an immediate defender with the ball towards the opposition goal. Interactions of attacker-defender dyads were filmed with player and ball displacement trajectories digitized using manual tracking software. One-way repeated measures analysis of variance was used to examine differences in mean defender-to-ball distance after this value had stabilized. Maximum attacker-to-ball distance was also compared as a function of proximity-to-goal. Significant differences were observed for defender-to-ball distance between locations (a) and (c) at the moment when the defender-to-ball distance had stabilized (a: 1.69 ± 0.64 m; c: 1.15 ± 0.59 m; P < 0.05). Findings indicate that proximity-to-goal influenced the performance of players, particularly when attacking or advancing away from goal areas, providing implications for training design in football. In this study, the task constraints of football revealed subtly different player interactions than observed in previous studies of dyadic systems in basketball and rugby union.

Wound healing angiogenesis : the clinical implications of a simple mathematical model

Nonhealing wounds are a major burden for health care systems worldwide. In addition, a patient who suffers from this type of wound usually has a reduced quality of life. While the wound healing process is undoubtedly complex, in this paper we develop a deterministic mathematical model, formulated as a system of partial differential equations, that focusses on an important aspect of successful healing: oxygen supply to the wound bed by a combination of diffusion from the surrounding unwounded tissue and delivery from newly formed blood vessels. While the model equations can be solved numerically, the emphasis here is on the use of asymptotic methods to establish conditions under which new blood vessel growth can be initiated and wound-bed angiogenesis can progress. These conditions are given in terms of key model parameters including the rate of oxygen supply and its rate of consumption in the wound. We use our model to discuss the clinical use of treatments such as hyperbaric oxygen therapy, wound bed debridement, and revascularisation therapy that have the potential to initiate healing in chronic, stalled wounds.

Mathematical modelling of tumour-induced angiogenesis

The growth of solid tumours beyond a critical size is dependent upon angiogenesis, the formation of new blood vessels from an existing vasculature. Tumours may remain dormant at microscopic sizes for some years before switching to a mode in which growth of a supportive vasculature is initiated. The new blood vessels supply nutrients, oxygen, and access to routes by which tumour cells may travel to other sites within the host (metastasize). In recent decades an abundance of biological research has focused on tumour-induced angiogenesis in the hope that treatments targeted at the vasculature may result in a stabilisation or regression of the disease: a tantalizing prospect. The complex and fascinating process of angiogenesis has also attracted the interest of researchers in the field of mathematical biology, a discipline that is, for mathematics, relatively new. The challenge in mathematical biology is to produce a model that captures the essential elements and critical dependencies of a biological system. Such a model may ultimately be used as a predictive tool. In this thesis we examine a number of aspects of tumour-induced angiogenesis, focusing on growth of the neovasculature external to the tumour. Firstly we present a one-dimensional continuum model of tumour-induced angiogenesis in which elements of the immune system or other tumour-cytotoxins are delivered via the newly formed vessels. This model, based on observations from experiments by Judah Folkman et al., is able to show regression of the tumour for some parameter regimes. The modelling highlights a number of interesting aspects of the process that may be characterised further in the laboratory. The next model we present examines the initiation positions of blood vessel sprouts on an existing vessel, in a two-dimensional domain. This model hypothesises that a simple feedback inhibition mechanism may be used to describe the spacing of these sprouts with the inhibitor being produced by breakdown of the existing vessel's basement membrane. Finally, we have developed a stochastic model of blood vessel growth and anastomosis in three dimensions. The model has been implemented in C++, includes an openGL interface, and uses a novel algorithm for calculating proximity of the line segments representing a growing vessel. This choice of programming language and graphics interface allows for near-simultaneous calculation and visualisation of blood vessel networks using a contemporary personal computer. In addition the visualised results may be transformed interactively, and drop-down menus facilitate changes in the parameter values. Visualisation of results is of vital importance in the communication of mathematical information to a wide audience, and we aim to incorporate this philosophy in the thesis. As biological research further uncovers the intriguing processes involved in tumourinduced angiogenesis, we conclude with a comment from mathematical biologist Jim Murray, Mathematical biology is : : : the most exciting modern application of mathematics.

The market structure and characteristics of electronic games

A multi-billion dollar industry, electronic games have been experiencing strong and rapid growth in recent times. The world of games is not only exciting due to the magnificent growth of the industry however, but due to a host of other factors. This chapter explores electronic games, providing an analysis of the industry, key motivators for game play, the game medium and academic research concerning the effects of play. It also reviews the emerging relationship games share with sport, recognizing that they can replicate sports, facilitate sports participation and be played as a sport. These are complex relationships that have not yet been comprehensively studied. The current chapter serves to draw academic attention to the area and presents ideas for future research.

Mathematical modelling of the drying of sol gel microspheres

This thesis presents a mathematical model of the evaporation of colloidal sol droplets suspended within an atmosphere consisting of water vapour and air. The main purpose of this work is to investigate the causes of the morphologies arising within the powder collected from a spray dryer into which the precursor sol for Synroc™ is sprayed. The morphology is of significant importance for the application to storage of High Level Liquid Nuclear Waste. We begin by developing a model describing the evaporation of pure liquid droplets in order to establish a framework. This model is developed through the use of continuum mechanics and thermodynamic theory, and we focus on the specific case of pure water droplets. We establish a model considering a pure water vapour atmosphere, and then expand this model to account for the presence of an atmospheric gas such as air. We model colloidal particle-particle interactions and interactions between colloid and electrolyte using DLVO Theory and reaction kinetics, then incorporate these interactions into an expression for net interaction energy of a single particle with all other particles within the droplet. We account for the flow of material due to diffusion, advection, and interaction between species, and expand the pure liquid droplet models to account for the presence of these species. In addition, the process of colloidal agglomeration is modelled. To obtain solutions for our models, we develop a numerical algorithm based on the Control Volume method. To promote numerical stability, we formulate a new method of convergence acceleration. The results of a MATLAB™ code developed from this algorithm are compared with experimental data collected for the purposes of validation, and further analysis is done on the sensitivity of the solution to various controlling parameters.

Mind games : applying White’s principles of narrative therapy to the creation of a cabaret about depression and bipolar disorder

This PhD represents my attempt to make sense of my personal experiences of depression through the form of cabaret. I first experienced depression in 2006. Previously, I had considered myself to be a happy and optimistic person. I found the experience of depression to be a shock: both in the experience itself, and also in the way it effected my own self image. These personal experiences, together with my professional history as a songwriter and cabaret performer, have been the motivating force behind the research project. This study has explored the question: What are the implications of applying principles of Michael White’s narrative therapy to the creation of a cabaret performance about depression and bipolar disorder? There is a 50 percent weighting on the creative work, the cabaret performance Mind Games, and a 50 percent weighting on the written exegesis. This research has focussed on the illustration of therapeutic principles in order to play games of truth within a cabaret performance. The research project investigates ways of telling my own story in relation to others’ stories through three re-authoring principles articulated in Michael White’s narrative therapy: externalisation, an autonomous ethic of living and rich descriptions. The personal stories presented in the cabaret were drawn from my own experiences and from interviews with individuals with depression or bipolar disorder. The cabaret focussed on the illustration of therapeutic principles, and was not focussed on therapeutic ends for myself or the interviewees. The research question has been approached through a methodology combining autoethnographic, practice-led and action research. Auto ethnographic research is characterised by close investigation of assumptions, attitudes, and beliefs. The combination of autoethnographic, practice-led, action research has allowed me to bring together personal experiences of mental illness, research into therapeutic techniques, social attitudes and public discourses about mental illness and forms of contemporary cabaret to facilitate the creation of a one-woman cabaret performance. The exegesis begins with a discussion of games of truth as informed by Michel Foucault and Michael White and self-stigma as informed by Michael White and Erving Goffman. These concepts form the basis for a discussion of my own personal experiences. White’s narrative therapy is focused on individuals re-authoring their stories, or telling their stories in different ways. White’s principles are influenced by Foucault’s notions of truth and power. Foucault’s term games of truth has been used to describe the effect of a ‘truth in flux’ that occurs through White’s re-authoring process. This study argues that cabaret is an appropriate form to represent this therapeutic process because it favours heightened performativity over realism, and showcases its ‘constructedness’ and artificiality. Thus cabaret is well suited to playing games of truth. A contextual review compares two major cabaret trends, personal cabaret and provocative cabaret, in reference to the performer’s relationship with the audience in terms of distance and intimacy. The study draws a parallel between principles of distance and intimacy in Michael White’s narrative therapy and relates these to performative terms of distance and intimacy. The creative component of this study, the cabaret Mind Games, used principles of narrative therapy to present the character ‘Jo’ playing games of truth through: externalising an aspect of her personality (externalisation); exploring different life values (an autonomous ethic of living); and enacting multiple versions of her identity (rich descriptions). This constant shifting between distance and intimacy within the cabaret created the effect of a truth in ‘constant flux’, to use one of White’s terms. There are three inter-related findings in the study. The first finding is that the application of principles of White’s narrative therapy was able to successfully combine provocative and empathetic elements within the cabaret. The second finding is that the personal agenda of addressing my own self-stigma within the project limited the effective portrayal of a ‘truth in flux’ within the cabaret. The third finding presents the view that the cabaret expressed ‘Jo’ playing games of truth in order to journey towards her own "preferred identity claim" (White 2004b) through an act of "self care" (Foucault 2005). The contribution to knowledge of this research project is the application of therapeutic principles to the creation of a cabaret performance. This process has focussed on creating a self-revelatory cabaret that questions notions of a ‘fixed truth’ through combining elements of existing cabaret forms in new ways. Two major forms in contemporary cabaret, the personal cabaret and the provocative cabaret use the performer-audience relationship in distinctive ways. Through combining elements of these two cabaret forms, I have explored ways to create a provocative cabaret focussed on the act of self-revelation.

Meeting under the “Omei” Tree in the Torres Strait Islands : networks and funds of knowledge of mathematical ideas

This paper focuses on the turning point experiences that worked to transform the researcher during a preliminary consultation process to seek permission to conduct of a small pilot project on one Torres Strait Island. The project aimed to learn from parents how they support their children in their mathematics learning. Drawing on a community research design, a consultative meeting was held with one Torres Strait Islander community to discuss the possibility of piloting a small project that focused on working with parents and children to learn about early mathematics processes. Preliminary data indicated that parents use networks in their community. It highlighted the funds of knowledge of mathematics that exist in the community and which are used to teach their children. Such knowledges are situated within a community’s unique histories, culture and the voices of the people. “Omei” tree means the Tree of Wisdom in the Island community.

Numerical simulation of a fractional mathematical model for epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider numerical simulation of fractional model based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in advection and diffusion terms belong to the intervals (0; 1) or (1; 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of the Riemann-Liouville and Gr¨unwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.